Modern paper and paper board is predominantly composed of a matrix of wood fibres. During the consolidation stage of papermaking, individual wet fibres are drawn and entangled together, forming a web structure. The deformability of the wet fibres used is a significant measure of the ability of the fibres to conform to each other by providing bonding contact in the course of dewatering, pressing, and drying. Fibre flexibility is a significant measure of fibre deformability. Fibres which are flexible are more conformable to one another, thus forming more contact area among fibres.
Fibre flexibility determines the total inter-fibre contact area and the voids in the fibre network, and plays a dominant role in determining most paper properties, such as bulk, permeability, opacity, surface smoothness, and physical strength.
There are several prior art apparatus and methods for measuring the flexibility of individual wet fibres.
The measurement of single fibre elastic modulus is usually performed by micro-tensile testing. The difficulties associated with this test are the dimensions of individual wood fibres, which are short (1-5 mm) and thin (10-30 um in diameter) and require careful handling and mounting techniques in sample preparation, and accurate measurements for stress and strain in a very small scale [1]. Because of the heterogeneous nature, a large population of fibres needs to be tested for the statistical analysis. Tedious and time-consuming operations in the fibre scale become a major drawback of this test method and make it impractical for engineering applications.
Some existing prior art methods treat the fibre as a cantilever [2-6]. Most of these methods are based on small deflection beam theory, which involves measuring the displacement of a fibre beam when applying a transverse force or bending moment on the fibre. If the fibre is treated as a beam subject to pure elastic deformation, the flexibility (F) of individual fibres can be defined as the reciprocal of its bending (also sometimes referred to as flexural stiffness) EI, where E is the elastic modulus of the fibre wall and I is the moment of inertia of the fibre cross-section: F=1/EI.
Seborg and Simmonds [8], for example, measured the stiffness of dry fibres by clamping individual fibres into place and then exerting a force on a fibre using a quartz spring to bend it like a cantilever beam. The flexural stiffness EI is determined from the slope of the load-deflection curve. The test suffers from two main disadvantages: (1) it is done on single fibres, making it very tedious and cumbersome; and (2) the clamping can damage the fibre.
James [8] calculated the fibre stiffness by measuring the resonance frequency of a fibre cantilever. Hydrodynamic or bending beam methods have also been developed for the fibre flexibility measurement by hydrodynamic forces generated by water flow and image analysis, so that individual fibre handling can be avoided.
Various apparatus have been developed for supporting the fibres. For example, Samuelsson [2] used a mechanical jaw to clamp fibres. Tam Doo and Kerekes [9] supported fibre on one end of a capillary tube so that mechanical damage to the fibre can be avoided. Like the Seborg and Simmonds method, the Tam Doo and Kerekes method is limited to testing individual fibres.
Kuhn et al. [5] developed a device that bends fibres by a T-junction tube when fibres in water flow out of a capillary. The fibre deformation is observed by a microscope and the force is calculated according to hydrodynamic theory. The Kuhn method is a direct measure of the flexibility of a fibre and may give flexibility results that are higher than expected [5].
Conformability testing as opposed to directly measuring flexibility is another typical method for fibre flexibility measurement. This method was first proposed by Mohlin [3]. In this method, wet pulp fibres are deposited onto a thin glass fibre (diameter=60 μm) that is fixed on a glass slide. The wet fibre arcs over the glass fibre and then is allowed to dry. The non-contact span, or freespan, length of the fibre is determined to calculate the fibre flexibility according to the beam deflection theory. Since only a conventional light microscope is required, and it can provide a numerical measure in an engineering unit, this method has commonly been used for fibre flexibility measurement [10-12]. No pressure, however, is applied to the fibre when taking the measurement and most likely does not approximate what happens in a paper structure of such fibres.
Steadman and Luner [6] have sought to improve upon the Mohlin method by taking the advantage that it does not need to handle individual fibres. In the Steadman method, a wire of 25 μm diameter was used as the support wire for forming the fibre arc over it.
In the Steadman method, fibres are deposited on a filter paper and wet pressed onto a thin support wire that is fixed on a glass slide. The fibre and the support wire are approximately 90 degrees to one another such that when pressed onto the wire, the fibre is subjected to a uniform distributed load and forms an arch-like span over the wire as it deforms. The fibre is then allowed to dry and the sections of the fibre in contact with the slide become adhered to the glass slide. The length of the section of the span not in contact with the glass slide, referred to as the non-contact span or freespan length, is measured from above using a conventional light microscope with incident lights, under which the optical contact zone of the fibre and the glass slide appears in dark, whereas the non-contact zone appears in light, thus the freespan length is measured. The freespan length measurement is then used in the calculation of flexibility according to the following formula:F=1/EI=72d/PWS4 Where E=modulus of elasticity (Nm−2)
I=moment of inertia (m4)
d=wire diameter (m)
P=pressing pressure (Nm−2)
W=projected fibre width (m)
S=mathematical estimate of the loaded span (m)
There are two important assumptions implied with this method: 1) the bonding strength between fibre and glass slide surface are high enough thus fibres are bonded on the glass slide at any place where they come into contact; 2) the freespan length of fibres remain unchanged while fibres are getting dried and after the pressure load is released. In practice, the fibre-glass surface bonding strength is not always sufficient to fix fibre on the glass slide, particularly for mechanical pulp fibres and unrefined chemical pulp fibres, which have much lower bonding strength compared with well refined chemical pulp fibres. Fibres that have high stiffness (low flexibility) have a higher tendency to spring back when external press load is removed, resulting in larger freespan or even totally becoming unbounded from the glass slide. For fibres that have low stiffness (high flexibility), the shape of the fibres arcing over the support can also be altered by the high surface tension while drying. All of these lead to an inaccurate measurement or are unable to conduct measurement for fibres that either have high stiffness and low bonding strength or have higher flexibility.